中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: 陈建毅 副教授 （青岛农业大学）
Inviter: 张志涛 研究员
Language: Chinese
Title: On Rabinowitz's minimal periodic solution conjecture for the wave equation in a disk
Time & Venue：2026年8月12日（星期三）9:00-10:00 南楼N820
Abstract: In this report, we talk about our recent work on Rabinowitz's minimal periodic solution conjecture for the wave equation in a disk. Firstly, under some suitable conditions for the defocusing wave equation, we prove that there exists a radial solution having minimal time-period. Secondly, we obtain a radially symmetric time-periodic solution for the focusing wave equation at the ground state level. Our method is based on a minimax theorem for the strongly indefinite variational problem and the spectral properties of the radial wave operator in a disk. This is joint work with Kui Li and Professor Zhitao Zhang.
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Speaker: 员兆阳 博士 （长安大学）
Inviter: 张志涛 研究员
Language: Chinese
Title: Normalized solutions to Schrodinger systems: attractive case and repulsive case
Time & Venue：2026年8月12日（星期三）11:00-12:00 南楼N820
Abstract: In this talk, we will introduce our recent work in normalized solutions to Schrodinger systems. More precisely, we focus on two cases: one is attractive case and the other is repulsive case. Based on the above two cases, we will prove the existence of normalized solutions by variational methods, especially for repulsive case, we will establish a new Liouville type theorems to avoid semi-trivial solutions.
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